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A253821 Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448). 3
1, 181, 589, 208489, 679321, 240595741, 783935461, 277647276241, 904660842289, 320404716185989, 1043977828065661, 369746764831354681, 1204749508926930121, 426687446210667115501, 1390279889323849293589, 492396943180345019933089, 1604381787530213157871201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of y being A253822.

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*(x^4+180*x^3-746*x^2+180*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

EXAMPLE

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

PROG

(PARI) Vec(-x*(x^4+180*x^3-746*x^2+180*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

CROSSREFS

Cf. A000567, A005448, A253822, A253823.

Sequence in context: A142391 A142552 A211553 * A154628 A142731 A229877

Adjacent sequences:  A253818 A253819 A253820 * A253822 A253823 A253824

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 14 2015

STATUS

approved

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Last modified June 1 20:49 EDT 2020. Contains 334765 sequences. (Running on oeis4.)