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A138289
Row sums of A138060.
2
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
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
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 02 2008
STATUS
approved