A081499 Sum at 45 degrees to horizontal in triangle of A081498.
1, 2, 4, 6, 8, 11, 12, 16, 15, 20, 16, 22, 14, 21, 8, 16, -3, 6, -20, -10, -44, -33, -76, -64, -117, -104, -168, -154, -230, -215, -304, -288, -391, -374, -492, -474, -608, -589, -740, -720, -889, -868, -1056, -1034, -1242, -1219, -1448, -1424, -1675, -1650, -1924, -1898, -2196, -2169, -2492, -2464, -2813
Offset: 1
Examples
a(7) = 7+5+2+(-2) = 12.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Programs
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Maple
seq((n+floor(n/2)+1)*(n-floor(n/2))/2-binomial(ceil(n/2)+1,ceil(n/2)-2),n=1..60); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
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Mathematica
LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,2,4,6,8,11,12},60] (* Harvey P. Dale, Jan 17 2022 *) -
PARI
Vec(x*(1 + x - x^2 - x^3 - x^4) / ((1 - x)^4*(1 + x)^3) + O(x^60)) \\ Colin Barker, Nov 12 2017
Formula
a(n) = (n+floor(n/2)+1)*(n-floor(n/2))/2-binomial(ceiling(n/2)+1, ceiling(n/2)-2). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
G.f.: x*(1 + x - x^2 - x^3 - x^4) / ((1 - x)^4*(1 + x)^3). - Colin Barker, Dec 18 2012
From Colin Barker, Nov 12 2017: (Start)
a(n) = (1/96)*(-2*n^3 + 36*n^2 + 32*n) for n even.
a(n) = (1/96)*(-2*n^3 + 30*n^2 + 50*n + 18) for n odd.
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.
(End)
Extensions
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
Comments