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A253822 Indices of centered triangular numbers (A005448) which are also octagonal numbers (A000567). 3
1, 256, 833, 294848, 960705, 340253760, 1108652161, 392652543616, 1279383632513, 453120695078528, 1476407603267265, 522900889468077120, 1703773094786790721, 603427173325465917376, 1966152674976353224193, 696354435116698200574208, 2268938483149616833927425 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of x being A253821.

LINKS

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

FORMULA

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(255*x^3+577*x^2-255*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

EXAMPLE

256 is in the sequence because the 256th centered triangular number is 97921, which is also the 181st octagonal number.

MATHEMATICA

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 256, 833, 294848, 960705}, 20] (* Harvey P. Dale, Jul 19 2019 *)

PROG

(PARI) Vec(x*(255*x^3+577*x^2-255*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

CROSSREFS

Cf. A000567, A005448, A253821, A253823.

Sequence in context: A195091 A203450 A188248 * A258733 A209381 A236987

Adjacent sequences:  A253819 A253820 A253821 * A253823 A253824 A253825

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 14 2015

STATUS

approved

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Last modified July 10 12:34 EDT 2020. Contains 335576 sequences. (Running on oeis4.)