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

Author

Ant King, Oct 26 2012

Keywords

• nonn
• easy
• changed

Examples

			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.
		

Links

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

Crossrefs

Cf. A002413, A218325.

Programs

Mathematica

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

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.

E.g.f.: 17 + exp(x)*(160*x^3 + 144*x^2 + 54*x - 51)/3. - Elmo R. Oliveira, Aug 23 2025