A256646 26-gonal pyramidal numbers: a(n) = n*(n+1)*(8*n-7)/2.

0, 1, 27, 102, 250, 495, 861, 1372, 2052, 2925, 4015, 5346, 6942, 8827, 11025, 13560, 16456, 19737, 23427, 27550, 32130, 37191, 42757, 48852, 55500, 62725, 70551, 79002, 88102, 97875, 108345, 119536, 131472, 144177, 157675, 171990, 187146, 203167, 220077

Offset

0,3

Comments

See comments in A256645.

References

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (24th row of the table).

Links

Luciano Ancora, Table of n, a(n) for n = 0..1000

Luciano Ancora, Polygonal and Pyramidal numbers, Section 3.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(1 + 23*x)/(1 - x)^4.

a(n) = A000292(n) + 23*A000292(n-1).

a(n) = n*A051866(n) - Sum_{i=0..n-1} A051866(i). - Bruno Berselli, Apr 09 2015

Sum_{n>=1} 1/a(n) = 2*(4*(sqrt(2)+1)*Pi - 4*(sqrt(2)-8)*log(2) + 8*sqrt(2)*log(sqrt(2)+2) - 7)/105. - Amiram Eldar, Jan 10 2022

E.g.f.: (1/2)*x*(2 + 25*x + 8*x^2)*exp(x). - G. C. Greubel, Jul 12 2024

Mathematica

Table[n (n + 1) (8 n - 7)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 27, 102}, 40] (* Vincenzo Librandi, Apr 08 2015 *)

Prog

(Magma) [n*(n+1)*(8*n-7)/2: n in [0..50]]; // Vincenzo Librandi, Apr 08 2015
(SageMath) [(8*n-7)*binomial(n+1, 2) for n in range(51)] # G. C. Greubel, Jul 12 2024

Crossrefs

Partial sums of A255185.

Cf. similar sequences listed in A237616.

Cf. A000292, A051866, A256645.

Sequence in context: A197619 A033659 A010015 * A323034 A031429 A154377

Adjacent sequences: A256643 A256644 A256645 * A256647 A256648 A256649

Keyword

nonn,easy

Author

Luciano Ancora, Apr 07 2015

Status

approved