

A168105


a(n) = sum of natural numbers m such that n  6 <= m <= n + 6.


1



21, 28, 36, 45, 55, 66, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741
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OFFSET

0,1


COMMENTS

Generalization: If a(n,k) = sum of natural numbers m such that n  k <= m <= n + k (k >= 1) then a(n,k) = (k + n)*(k + n + 1)/2 = A000217(k+n) for 0 <= n <= k, a(n,k) = a(n1,k) +2k + 1 = ((k + n  1)*(k + n)/2) + 2k + 1 = A000217(k+n1) +2k +1 for n >= k + 1 (see, e.g., A008486).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = (6 + n)*(7 + n)/2 = A000217(6+n) for 0 <= n <= 6, a(n) = a(n1) + 13 for n >= 7.
G.f.: (21  35*x + 15*x^2  x^8)/(1  x)^3.  G. C. Greubel, Jul 13 2016


MATHEMATICA

CoefficientList[Series[(21  35*x + 15*x^2  x^8)/(1  x)^3, {x, 0, 50}], x] (* G. C. Greubel, Jul 13 2016 *)


PROG

(PARI) a(n)=if(n>5, 13*n, n*(n+13)/2+21) \\ Charles R Greathouse IV, Jul 13 2016


CROSSREFS

Sequence in context: A120735 A009727 A337702 * A227936 A048012 A254368
Adjacent sequences: A168102 A168103 A168104 * A168106 A168107 A168108


KEYWORD

nonn,easy


AUTHOR

Jaroslav Krizek, Nov 18 2009


STATUS

approved



