A218324 Odd heptagonal pyramidal numbers.

1, 115, 645, 1911, 4233, 7931, 13325, 20735, 30481, 42883, 58261, 76935, 99225, 125451, 155933, 190991, 230945, 276115, 326821, 383383, 446121, 515355, 591405, 674591, 765233, 863651, 970165, 1085095, 1208761, 1341483, 1483581, 1635375, 1797185, 1969331

Offset

1,2

Links

Table of n, a(n) for n=1..34.

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

Formula

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 320.

a(n) = (2*n-1)*(4*n-3)*(20*n-17)/3.

G.f.: x*(1 + 111*x + 191*x^2 + 17*x^3)/(1-x)^4.

Example

The sequence of heptagonal pyramidal numbers A002413 begins 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, ... . As the third odd term is 645, a(3) = 645.

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 115, 645, 1911}, 34]

Crossrefs

Cf. A002413, A218325.

Sequence in context: A255143 A154070 A251215 * A258673 A287430 A256889

Adjacent sequences: A218321 A218322 A218323 * A218325 A218326 A218327

Keyword

nonn,easy

Author

Ant King, Oct 26 2012

Status

approved