A264888 a(n) = n*(n + 1)*(13*n^2 + 13*n - 14)/24.

0, 1, 16, 71, 205, 470, 931, 1666, 2766, 4335, 6490, 9361, 13091, 17836, 23765, 31060, 39916, 50541, 63156, 77995, 95305, 115346, 138391, 164726, 194650, 228475, 266526, 309141, 356671, 409480, 467945, 532456, 603416, 681241, 766360, 859215, 960261, 1069966

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2015

Keywords

• nonn
• easy

Comments

Partial sum of centered 13-gonal (or tridecagonal) pyramidal numbers.

This is the case k=13 of the formula n*(n + 1)*(k*n^2 + k*n - 2*k + 12)/24.

Links

• OEIS Wiki, Figurate numbers
• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A062025.

Cf. similar sequences listed in A264854.

Programs

Mathematica

Table[n (n + 1) (13 n^2 + 13 n - 14)/24, {n, 0, 50}]

PARI

a(n)=n*(n+1)*(13*n^2+13*n-14)/24 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: x*(1 + 11*x + x^2)/(1 - x)^5.

a(n) = Sum_{k = 0..n} A062025(k).