A138289 Row sums of A138060.

1, 3, 6, 10, 11, 14, 20, 30, 41, 55, 75, 105, 146, 201, 276, 381, 527, 728, 1004, 1385, 1912, 2640, 3644, 5029, 6941, 9581, 13225, 18254, 25195, 34776, 48001, 66255, 91450, 126226, 174227, 240482, 331932, 458158, 632385, 872867, 1204799, 1662957, 2295342, 3168209, 4373008, 6035965, 8331307, 11499516

Offset

1,2

Links

Table of n, a(n) for n=1..48.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1).

Formula

Conjecture: a(n) = a(n-1) + a(n-4) with g.f. x*(-1 - 2*x - 3*x^2 - 4*x^3) / (-1 + x + x^4). - R. J. Mathar, Jul 08 2011

From Charlie Neder, Jun 22 2018: (Start)

The conjectured recurrence is true. Proof:

Denote by W(n) the word formed from the n-th row of A138060 and by M^k() the morphism sending W(n) to W(n+1) applied k times. We have W(5) = W(4) + W(1), so for any k >= 0, W(k+5) = M^k(W(5)) = M^k(W(4) + W(1)) = M^k(W(4)) + M^k(W(1)) = W(k+4) + W(k+1).

Setting n=k+5 completes the proof. (End)

Maple

A138060 := proc() option remember; if n = 1 then return [1] ; else  L := procname(n-1) ; a := [] ; for i from 1 to nops(L) do if op(i, L) = 1 then a := [op(a), 1, 2] ; elif op(i, L) <=3 then a := [op(a), op(i, L)+1] ; else a := [op(a), 1] ; end if; end do: end if; a ; end proc:
A138289 := proc(n) add(k, k=A138060(n)) ; end proc: # R. J. Mathar, Jul 08 2011

Mathematica

LinearRecurrence[{1, 0, 0, 1}, {1, 3, 6, 10}, 35] (* Jean-François Alcover, Jul 01 2023 *)

Crossrefs

Sequence in context: A231668 A123053 A221129 * A219638 A105359 A105355

Adjacent sequences: A138286 A138287 A138288 * A138290 A138291 A138292

Keyword

nonn

Author

Roger L. Bagula, May 02 2008

Status

approved