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A253460 Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844). 4
1, 16, 112, 3937, 28321, 999856, 7193296, 253959361, 1827068737, 64504677712, 464068265776, 16383934179361, 117871512438241, 4161454776879856, 29938900091047312, 1056993129393303937, 7604362751613578881, 268472093411122320016, 1931478200009757988336 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of x being A253459.
LINKS
FORMULA
a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+15*x^3-158*x^2+15*x+1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).
a(n) = A105040(n) + 1. - Michel Marcus, Mar 12 2024
EXAMPLE
16 is in the sequence because the 16th centered heptagonal number is 841, which is also the 21st centered square number.
PROG
(PARI) Vec(-x*(x^4+15*x^3-158*x^2+15*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A205964 A222113 A229531 * A081194 A121148 A091031
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 01 2015
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)