

A131023


First subdiagonal of triangular array T: T(j,1) = 1 for ((j1) mod 6) < 3, else 0; T(j,k) = T(j1,k1) + T(j1,k) for 2 <= k <= j.


4



1, 2, 3, 4, 5, 7, 14, 37, 101, 256, 593, 1267, 2534, 4825, 8921, 16384, 30581, 58975, 117950, 242461, 504605, 1048576, 2156201, 4371451, 8742902, 17308657, 34085873, 67108864, 132623405, 263652487, 527304974, 1059392917, 2133134741
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OFFSET

1,2


COMMENTS

Also first differences of main diagonal A129339.


LINKS

Table of n, a(n) for n=1..33.
Index to sequences with linear recurrences with constant coefficients, signature (5,9,6).


FORMULA

a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4; for n > 4, a(n) = 5*a(n1)  9*a(n2) + 6*a(n3).
G.f.: x*(13*x+2*x^2 +x^3)/((12*x)*(13*x+3*x^2)).
a(n) = A057681(n1)+2^(n2), a(1) = 1.  Bruno Berselli, Feb 17 2011


EXAMPLE

For first seven rows of T see A131022 or A129339.


PROG

(MAGMA) m:=34; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j1) mod 6 lt 3 then M[j, 1]:=1; end if; end for; for k:=2 to m do for j:=k to m do M[j, k]:=M[j1, k1]+M[j, k1]; end for; end for; [ M[n+1, n]: n in [1..m1] ];
(PARI) {m=33; v=concat([1, 2, 3, 4], vector(m4)); for(n=5, m, v[n]=5*v[n1]9*v[n2]+6*v[n3]); v}


CROSSREFS

Cf. A131022 (T read by rows), A129339 (main diagonal of T), A131024 (row sums of T), A131025 (antidiagonal sums of T). First through sixth column of T are in A088911, A131026, A131027, A131028, A131029, A131030 resp.
Sequence in context: A037398 A048331 A133476 * A069514 A249155 A101012
Adjacent sequences: A131020 A131021 A131022 * A131024 A131025 A131026


KEYWORD

nonn,easy


AUTHOR

Klaus Brockhaus, following a suggestion of Paul Curtz, Jun 10 2007


STATUS

approved



