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A193608
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The consecutive squares of numbers multiplied by their next consecutive integer.
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1
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15, 52, 125, 246, 427, 680, 1017, 1450, 1991, 2652, 3445, 4382, 5475, 6736, 8177, 9810, 11647, 13700, 15981, 18502, 21275, 24312, 27625, 31226, 35127, 39340, 43877, 48750, 53971, 59552, 65505, 71842, 78575, 85716, 93277, 101270, 109707, 118600
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OFFSET
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1,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = (n+2)*(n^2 + (n+1)^2).
G.f.: x*(3-x)*(5-x+2*x^2)/(1-x)^4. [Colin Barker, Mar 28 2012]
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MATHEMATICA
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Table[2*(n + 1)^3 - n, {n, 38}] (* L. Edson Jeffery, Jan 11 2018 *)
LinearRecurrence[{4, -6, 4, -1}, {15, 52, 125, 246}, 40] (* Harvey P. Dale, May 01 2022 *)
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PROG
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(C)
int a(int n)
{
return ((n+2)*((n*n)*((n+1)*(n+1))));
}
(PARI) a(n)=2*n^3+6*n^2+5*n+2 \\ Charles R Greathouse IV, Jul 31 2011
(MAGMA) [(n+2)*(n^2 + (n+1)^2): n in [1..40] ]; // Vincenzo Librandi, Aug 01 2011
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CROSSREFS
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Sequence in context: A015234 A295339 A346824 * A346857 A332394 A220156
Adjacent sequences: A193605 A193606 A193607 * A193609 A193610 A193611
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KEYWORD
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nonn,easy
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AUTHOR
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Ankur Trapasiya, Jul 31 2011
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STATUS
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approved
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