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A213581
Antidiagonal sums of the convolution array A213571.
4
1, 8, 36, 124, 367, 988, 2498, 6048, 14197, 32576, 73472, 163508, 360027, 785908, 1703294, 3669240, 7863393, 16776120, 35650300, 75495980, 159381831, 335542348, 704640826, 1476392464, 3087004877, 6442447728, 13421769208
OFFSET
1,2
FORMULA
a(n) = 8*a(n-1) - 26*a(n-2) + 44*a(n-3) - 41*a(n-4) + 20*a(n-5) - 4*a(n-6).
G.f.: f(x)/g(x), where f(x) = x*(1 - 2*x^2) and g(x) = (1 - x)^4*(1 - 2*x)^2.
a(n) = 8 +(n-2)*2^(n+2) -(n-2)*n*(n+5)/6. - Bruno Berselli, Jul 09 2012
MATHEMATICA
(* First Program *)
b[n_]:= n; c[n_]:= -1 + 2^n;
t[n_, k_]:= Sum[b[k-i] c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:= Table[t[n, k], {k, 1, 60}] (* A213571 *)
d = Table[t[n, n], {n, 1, 40}] (* A213572 *)
s[n_]:= Sum[t[i, n+1-i], {i, 1, n}]
s1 = Table[s[n], {n, 1, 50}] (* A213581 *)
(* Second program *)
Table[2^(n+2)*(n-2) - (n^3+3*n^2-10*n-48)/6, {n, 35}] (* G. C. Greubel, Jul 26 2019 *)
PROG
(PARI) vector(35, n, 2^(n+2)*(n-2) - (n^3+3*n^2-10*n-48)/6) \\ G. C. Greubel, Jul 26 2019
(Magma) [2^(n+2)*(n-2) - (n^3+3*n^2-10*n-48)/6: n in [1..35]]; // G. C. Greubel, Jul 26 2019
(Sage) [2^(n+2)*(n-2) - (n^3+3*n^2-10*n-48)/6 for n in (1..35)] # G. C. Greubel, Jul 26 2019
(GAP) List([1..35], n-> 2^(n+2)*(n-2) - (n^3+3*n^2-10*n-48)/6); # G. C. Greubel, Jul 26 2019
CROSSREFS
Sequence in context: A054470 A347751 A341222 * A276279 A210379 A131123
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 19 2012
STATUS
approved