A304659 a(n) = n*(n + 1)*(16*n - 1)/6.

0, 5, 31, 94, 210, 395, 665, 1036, 1524, 2145, 2915, 3850, 4966, 6279, 7805, 9560, 11560, 13821, 16359, 19190, 22330, 25795, 29601, 33764, 38300, 43225, 48555, 54306, 60494, 67135, 74245, 81840, 89936, 98549, 107695, 117390, 127650, 138491, 149929, 161980, 174660, 187985

Offset: 0

Author

Bruno Berselli, May 22 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A007742, A076455, A139273 (first differences).

First lower diagonal of the rectangular array in A213835.

Programs

Magma

[n*(n+1)*(16*n-1)/6: n in [0..41]]; // Vincenzo Librandi, May 23 2018

Mathematica

Table[n (n + 1) (16 n - 1)/6, {n, 0, 50}]

PARI

concat(0, Vec(x*(5 + 11*x) / (1 - x)^4 + O(x^40))) \\ Colin Barker, May 25 2018

Formula

O.g.f.: x*(5 + 11*x)/(1 - x)^4.

E.g.f.: x*(30 + 63*x + 16*x^2)*exp(x)/6.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) + a(-n) = A033429(n).

a(n) = n*A007742(n) - Sum_{k = 0..n-1} A007742(k) for n > 0.

Also, this sequence is related to A076455 by the same type of recurrence:

A076455(n) = n*a(n) - Sum_{k = 0..n-1} a(k) for n > 0.