A131075 First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.

1, 2, 4, 7, 11, 16, 22, 30, 46, 92, 232, 628, 1652, 4096, 9544, 21000, 43912, 87824, 169120, 315952, 578096, 1048576, 1913440, 3567072, 6874336, 13748672, 28384384, 59797312, 126906176, 268435456, 561834112, 1158971520, 2353246336, 4706492672, 9292452352

Offset

1,2

Comments

Also first differences of main diagonal A129961.

Links

Table of n, a(n) for n=1..35.

Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-10,4).

Formula

a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 7, a(5) = 11; for n > 5, a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-10*a(n-4)+4*a(n-5).

G.f.: x*(1-4*x+6*x^2-5*x^3+3*x^4)/((1-2*x)*(1-4*x+6*x^2-4*x^3+2*x^4)).

Example

For first seven rows of T see A131074 or A129961.

Prog

(Magma) m:=34; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) mod 8 lt 4 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[j-1, k-1]+M[j, k-1]; end for; end for; [ M[n+1, n]: n in [1..m-1] ];
(PARI) lista(m) = my(v=concat([1, 2, 4, 7, 11], vector(m-5))); for(n=6, m, v[n]=6*v[n-1]-14*v[n-2]+16*v[n-3]-10*v[n-4]+4*v[n-5]); v

Crossrefs

Cf. A131074 (T read by rows), A129961 (main diagonal of T), A131076 (row sums of T), A131077 (antidiagonal sums of T). First through sixth column of T are in A131078, A131079, A131080, A131081, A131082, A131083 resp.

Sequence in context: A177176 A005689 A212365 * A365698 A133523 A114805

Adjacent sequences: A131072 A131073 A131074 * A131076 A131077 A131078

Keyword

nonn,easy

Author

Klaus Brockhaus, following a suggestion of Paul Curtz, Jun 14 2007

Status

approved