A264854 a(n) = n*(n + 1)*(11*n^2 + 11*n - 10)/24.

0, 1, 14, 61, 175, 400, 791, 1414, 2346, 3675, 5500, 7931, 11089, 15106, 20125, 26300, 33796, 42789, 53466, 66025, 80675, 97636, 117139, 139426, 164750, 193375, 225576, 261639, 301861, 346550, 396025, 450616, 510664, 576521, 648550, 727125, 812631, 905464, 1006031

Offset: 0

Author

Ilya Gutkovskiy, Nov 26 2015

Keywords

• nonn
• easy

Comments

Partial sums of centered 11-gonal (or hendecagonal) pyramidal numbers.

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. A004467.

Cf. similar sequences provided by the partial sums of centered k-gonal pyramidal numbers: A006522 (k=1), A006007 (k=2), A002817 (k=3), A006325 (k=4), A006322 (k=5), A000537 (k=6), A006323 (k=7), A006324 (k=8), A236770 (k=9), A264853 (k=10), this sequence (k=11), A062392 (k=12), A264888 (k=13).

Programs

Magma

[n*(n+1)*(11*n^2+11*n-10)/24: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015

Mathematica

Table[n (n + 1) (11 n^2 + 11 n - 10)/24, {n, 0, 50}]

PARI

a(n)=n*(n+1)*(11*n^2+11*n-10)/24 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: x*(1 + 9*x + x^2)/(1 - x)^5.

a(n) = Sum_{k = 0..n} A004467(k).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015