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A254709 Indices of pentagonal numbers (A000326) which are also centered square numbers (A001844). 3
1, 2, 10, 25, 137, 346, 1906, 4817, 26545, 67090, 369722, 934441, 5149561, 13015082, 71724130, 181276705, 998988257, 2524858786, 13914111466, 35166746297, 193798572265, 489809589370, 2699265900242, 6822167504881, 37595924031121, 95020535478962 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of y being A254710.
LINKS
FORMULA
a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+x^3-6*x^2+x+1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).
EXAMPLE
10 is in the sequence because the 10th pentagonal number is 145, which is also the 9th centered square number.
MATHEMATICA
LinearRecurrence[{1, 14, -14, -1, 1}, {1, 2, 10, 25, 137}, 30] (* Harvey P. Dale, Aug 08 2017 *)
PROG
(PARI) Vec(-x*(x^4+x^3-6*x^2+x+1)/((x-1)*(x^2-4*x+1)*(x^2+4*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A058373 A167386 A027719 * A069894 A045605 A294871
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 06 2015
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)