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A271995
The Pnictogen sequence: a(n) = A018227(n)-3.
2
7, 15, 33, 51, 83, 115, 165, 215, 287, 359, 457, 555, 683, 811, 973, 1135, 1335, 1535, 1777, 2019, 2307, 2595, 2933, 3271, 3663, 4055, 4505, 4955, 5467, 5979, 6557, 7135, 7783, 8431, 9153, 9875, 10675, 11475, 12357, 13239, 14207, 15175, 16233, 17291, 18443
OFFSET
2,1
COMMENTS
Terms up to 115 are the atomic numbers of the elements of group 15 in the periodic table. Those elements are also known as pnictogens.
FORMULA
From Colin Barker, Jun 19 2016, corrected Jun 26 2016: (Start)
a(n) = (6*(-7+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12.
a(n) = (n^3+6*n^2+14*n-18)/6 for n even.
a(n) = (n^3+6*n^2+11*n-24)/6 for n odd.
a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6) for n>7.
G.f.: x^2*(7+x-4*x^2-2*x^3+x^4+x^5) / ((1-x)^4*(1+x)^2).
(End)
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {7, 15, 33, 51, 83, 115}, 50] (* Harvey P. Dale, Oct 29 2023 *)
PROG
(PARI) Vec(x^2*(7+x-4*x^2-2*x^3+x^4+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jun 19 2016, corrected Jun 26 2016
CROSSREFS
Cf. A018227.
Sequence in context: A159695 A014001 A291642 * A174792 A063592 A159792
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jun 18 2016
STATUS
approved