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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..32.

FORMULA

G.f.: (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)).

EXAMPLE

For first seven rows of T see A131022 or A129339.

PROG

(PARI) {m=32; 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]), ", "))}

(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] ];

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.

Sequence in context: A001618 A118027 A082644 * A053982 A118000 A121640

Adjacent sequences:  A131021 A131022 A131023 * A131025 A131026 A131027

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 26 15:53 EDT 2021. Contains 347668 sequences. (Running on oeis4.)