A131024 Row sums of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j-1,k) for 2 <= k <= j.

1, 3, 7, 11, 16, 22, 36, 73, 175, 431, 1024, 2290, 4824, 9649, 18571, 34955, 65536, 124510, 242460, 484921, 989527, 2038103, 4194304, 8565754, 17308656, 34617313, 68703187, 135812051, 268435456, 532087942, 1059392916, 2118785833, 4251920575, 8546887871

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

Sum of n-th row equals (n+1)-th term of main diagonal minus (n+1)-th term of first column. A088911 has offset 0, so a(n) = A129339(n+1) - A088911(n).

Examples

			For first seven rows of T see A131022 or A129339.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-14,14,0,-14,15,-6).

Crossrefs

Cf. A131022 (T read by rows), A129339 (main diagonal of T), A131023 (first subdiagonal of T), A131025 (antidiagonal sums of T). First through sixth column of T are in A088911, A131026, A131027, A131028, A131029, A131030 resp.

Programs

Magma

m:=32; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) 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[j-1, k-1]+M[j, k-1]; end for; end for; [ &+[ M[j, k]: k in [1..j] ]: j in [1..m] ];

PARI

lista(m) = my(M=matrix(m, m)); for(j=1, m, M[j, 1]=if((j-1)%6<3, 1, 0)); for(k=2, m, for(j=k, m, M[j, k]=M[j-1, k-1]+M[j, k-1])); for(j=1, m, print1(sum(k=1, j, M[j, k]), ", "))

Formula

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