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A274221 List of quadruples: 3*n*(3*n-1), 3*n*(3*n+1), (3*n+1)^2, (3*n+2)^2. 2
0, 0, 1, 4, 6, 12, 16, 25, 30, 42, 49, 64, 72, 90, 100, 121, 132, 156, 169, 196, 210, 240, 256, 289, 306, 342, 361, 400, 420, 462, 484, 529, 552, 600, 625, 676, 702, 756, 784, 841, 870, 930, 961, 1024, 1056, 1122, 1156, 1225, 1260, 1332, 1369, 1444, 1482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For the formulae of the permutations of A152743, A045945, A016778 and A016790, see the link.

LINKS

Table of n, a(n) for n=0..52.

Luce ETIENNE, Permutations

FORMULA

G.f.: x^2*(1+3*x+x^2+3*x^3+x^4)/((1-x)^3*(1+x)^2*(1+x^2)). - Robert Israel, Sep 15 2016

a(n) = (18*n^2-18*n+1-3*(2*n-1)*(-1)^n-4*(-1)^((2*n-1+(-1)^n)/4))/32. Therefore: a(2k) = (18*k^2-12*k+1-(-1)^k)/8, a(2k+1) = (18*k^2+12*k+1-(-1)^k)/8.

a(n) = A064412(n) - A269064(n) for n>0.

MATHEMATICA

Flatten[Table[{3 n (3 n - 1), 3 n (3 n + 1), (3 n + 1)^2, (3 n + 2)^2}, {n, 0, 15}]] (* Bruno Berselli, Sep 15 2016 *)

PROG

(MAGMA) &cat [[3*n*(3*n-1), 3*n*(3*n+1), (3*n+1)^2, (3*n+2)^2]: n in [0..15]]; // Bruno Berselli, Sep 15 2016

CROSSREFS

Cf. A152743, A045945, A016778, A016790, A064412, A269064.

Sequence in context: A310598 A024904 A172445 * A327479 A139056 A152519

Adjacent sequences:  A274218 A274219 A274220 * A274222 A274223 A274224

KEYWORD

nonn,easy

AUTHOR

Luce ETIENNE, Sep 14 2016

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)