A213759 Principal diagonal of the convolution array A213783.

1, 4, 11, 22, 39, 62, 93, 132, 181, 240, 311, 394, 491, 602, 729, 872, 1033, 1212, 1411, 1630, 1871, 2134, 2421, 2732, 3069, 3432, 3823, 4242, 4691, 5170, 5681, 6224, 6801, 7412, 8059, 8742, 9463, 10222, 11021, 11860, 12741, 13664, 14631

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

a(n) = (3 - 3*(-1)^n - 4*n + 18*n^2 + 4*n^3)/24.

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).

G.f.: x*(1 + x + x^2 - x^3)/((1 - x)^4 *(1 + x)).

a(n+1) = a(n) + A047838(n+2) for n > 0. - Guenther Schrack, May 24 2018

a(n) = A212964(n+2) - n for n > 0. - Guenther Schrack, May 30 2018

Mathematica

b[n_] := Floor[(n + 2)/2]; c[n_] := Floor[(n + 1)/2];
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}]  (* A213783 *)
Table[t[n, n], {n, 1, 40}] (* A213759 *)
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 4, 11, 22, 39}, 50] (* Harvey P. Dale, Jul 22 2014 *)

Crossrefs

Cf. A213783, A213500.

Partial sums of A047838. - Guenther Schrack, May 24 2018

Sequence in context: A301082 A008247 A016435 * A047951 A132072 A009846

Adjacent sequences: A213756 A213757 A213758 * A213760 A213761 A213762

Keyword

nonn,easy

Author

Clark Kimberling, Jun 22 2012

Status

approved