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A183207 Termwise products of the natural numbers and odd integers repeated 5
1, 2, 9, 12, 25, 30, 49, 56, 81, 90, 121, 132, 169, 182, 225, 240, 289, 306, 361, 380, 441, 462, 529, 552, 625, 650, 729, 756, 841, 870, 961, 992, 1089, 1122, 1225, 1260, 1369, 1406, 1521, 1560, 1681, 1722, 1849, 1892, 2025 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There is a chessboard of n^2 squares. A pawn is standing on the lower left corner of the chessboard O (0,0) and its primary goal is to reach the upper right corner of the  chessboard N (n,n). The only moves allowed are diagonal shortcuts through squares. Once a square is crossed it is destroyed so that it is impossible to cross again. The secondary goal of the pawn on its way to N is to destroy as many squares as possible. a(n) is the maximum possible number of destroyed squares, provided the pawn has reached its primary goal. - Ivan N. Ianakiev, Feb 23 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1)

FORMULA

Termwise products of (1, 2, 3, 4, 5, 6, 7, 8...) and (1, 1, 3, 3, 5, 5, 7, 7,...).

G.f. x*( -1-x-5*x^2-x^3 ) / ( (1+x)^2*(x-1)^3 ). a(n) = n^2-n*(1+(-1)^n)/2. - R. J. Mathar, Feb 12 2011

EXAMPLE

a(4) = 4*3 = 12.

MATHEMATICA

f[n_] := n (2 Floor[(n - 1)/2] + 1); Array[f, 45] (* Robert G. Wilson v, Feb 11 2011 *)

CoefficientList[Series[(-1 - x - 5 x^2 - x^3)/((1 + x)^2 (x - 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 23 2014 *)

PROG

(PARI) a(n) = n^2-n*(1+(-1)^n)/2

(MAGMA) I:=[1, 2, 9, 12, 25]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..60]]; // Vincenzo Librandi, Feb 23 2014

CROSSREFS

Cf. A093005.

Sequence in context: A273669 A129829 A053900 * A178312 A253608 A126977

Adjacent sequences:  A183204 A183205 A183206 * A183208 A183209 A183210

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Feb 11 2011

STATUS

approved

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Last modified November 19 11:04 EST 2017. Contains 294936 sequences.