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A069190
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Centered 24-gonal numbers.
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19
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1, 25, 73, 145, 241, 361, 505, 673, 865, 1081, 1321, 1585, 1873, 2185, 2521, 2881, 3265, 3673, 4105, 4561, 5041, 5545, 6073, 6625, 7201, 7801, 8425, 9073, 9745, 10441, 11161, 11905, 12673, 13465, 14281, 15121, 15985, 16873, 17785, 18721, 19681, 20665, 21673
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OFFSET
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1,2
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COMMENTS
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Sequence found by reading the line from 1, in the direction 1, 25, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Semi-axis opposite to A135453 in the same spiral. - Omar E. Pol, Sep 16 2011
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LINKS
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FORMULA
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a(n) = 12*n^2 - 12*n + 1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=25, a(3)=73. - Harvey P. Dale, Jul 17 2011
Binomial transform of [1, 24, 24, 0, 0, 0, ...] and Narayana transform (cf. A001263) of [1, 24, 0, 0, 0, ...]. - Gary W. Adamson, Jul 26 2011
Sum_{n>=1} 1/a(n) = Pi*tan(Pi/sqrt(6))/(4*sqrt(6)).
Sum_{n>=1} a(n)/n! = 13*e - 1.
Sum_{n>=1} (-1)^n * a(n)/n! = 13/e - 1. (End)
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EXAMPLE
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a(5) = 241 because 12*5^2 - 12*5 + 1 = 300 - 60 + 1 = 241.
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MATHEMATICA
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Table[12n^2-12n+1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 25, 73}, 50] (* Harvey P. Dale, Jul 17 2011 *)
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PROG
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CROSSREFS
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Cf. centered k-gonal numbers with k=3..25: A005448, A001844, A005891, A003215, A069099, A016754, A060544, A062786, A069125, A003154, A069126, A069127, A069128, A069129, A069130, A069131, A069132, A069133, A069178, A069173, A069174, A069190, A262221.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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