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A253599 Centered square numbers (A001844) which are also centered heptagonal numbers (A069099). 3
1, 841, 43513, 54236113, 2807177521, 3498988573081, 181102250526121, 225733748749491361, 11683630587634972513, 14562987063325697070313, 753757743549580366157401, 939516547177660272044661361, 48627927055673997154643575441, 60611970510056587727363585953081 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+840*x^3-21842*x^2+840*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).
EXAMPLE
841 is in the sequence because it is the 21st centered square number and the 16th centered heptagonal number.
MATHEMATICA
LinearRecurrence[{1, 64514, -64514, -1, 1}, {1, 841, 43513, 54236113, 2807177521}, 20] (* Harvey P. Dale, Mar 26 2023 *)
PROG
(PARI) Vec(-x*(x^4+840*x^3-21842*x^2+840*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A108324 A133496 A361675 * A121499 A253514 A342841
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 05 2015
STATUS
approved

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Last modified June 12 14:48 EDT 2024. Contains 373331 sequences. (Running on oeis4.)