A017642 -id:A017642 - cp's OEIS frontend

1000, 10648, 39304, 97336, 195112, 343000, 551368, 830584, 1191016, 1643032, 2197000, 2863288, 3652264, 4574296, 5639752, 6859000, 8242408, 9800344, 11543176, 13481272, 15625000, 17984728, 20570824, 23393656, 26463592, 29791000, 33386248, 37259704

Offset: 0

N. J. A. Sloane

6n + 5 = (12n + 10) / 2 is never a square, as 5 is not a quadratic residue modulo 6. Using this, we can show that each term has an even square part and an even squarefree part, neither part being a power of 2. (Less than 2% of integers have this property - see A339245.) - Peter Munn, Dec 14 2020

Eric Weisstein's World of Mathematics, Quadratic Residue.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

A000578, A017641 are used in a formula defining this sequence.
Subsequence of A339245.
Cf. A017642, A017644.

A017643:=(12*n+10)^3; seq(A017643(n), n=0..100); # Wesley Ivan Hurt, Nov 25 2013

(12Range[0,30]+10)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{1000,10648,39304,97336},30] (* Harvey P. Dale, Sep 30 2011 *)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1000, a(1)=10648, a(2)=39304, a(3)=97336. [Harvey P. Dale, Sep 30 2011]

a(n) = A017641(n)^3 = A000578(A017641(n)). - Michel Marcus, Nov 25 2013

cp's OEIS Frontend

A017643 a(n) = (12n+10)^3.

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