A253121 Numbers k such that the hexagonal number H(k) is equal to the sum of the octagonal numbers O(m), O(m+1), O(m+2) and O(m+3) for some m.

18, 1730, 169498, 16609050, 1627517378, 159480093970, 15627421691658, 1531327845688490, 150054501455780338, 14703809814820784610, 1440823307350981111418, 141185980310581328134330, 13834785247129619176052898, 1355667768238392097925049650

Offset

1,1

Comments

Also positive integers y in the solutions to 24*x^2-4*y^2+56*x+2*y+60 = 0, the corresponding values of x being A253120.

Links

Colin Barker, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Formula

a(n) = 99*a(n-1)-99*a(n-2)+a(n-3).

G.f.: -2*x*(5*x^2-26*x+9) / ((x-1)*(x^2-98*x+1)).

Example

18 is in the sequence because H(18) = 630 = 96+133+176+225 = O(6)+O(7)+O(8)+O(9).

Prog

(PARI) Vec(-2*x*(5*x^2-26*x+9)/((x-1)*(x^2-98*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A000567, A253120.

Sequence in context: A086366 A086193 A064347 * A067303 A055740 A072477

Adjacent sequences: A253118 A253119 A253120 * A253122 A253123 A253124

Keyword

nonn,easy

Author

Colin Barker, Dec 27 2014

Status

approved