A034943 -id:A034943 - cp's OEIS frontend

A106688 Six-symbol substitution: characteristic polynomial: x^6 - 4x^4 - 3x^3 - x - 1.

2, 4, 2, 5, 6, 3, 4, 3, 6, 1, 4, 5, 2, 4, 2, 5, 6, 2, 4, 1, 4, 5, 2, 2, 5, 6, 3, 6, 3, 4, 2, 5, 6, 3, 4, 3, 6, 1, 4, 5, 3, 4, 2, 5, 6, 2, 2, 5, 6, 3, 6, 3, 4, 3, 4, 3, 6, 1, 4, 5, 2, 4, 1, 4, 5, 2, 4, 2, 5, 6, 3, 4, 3, 6, 1, 4, 5, 2, 4, 2, 5, 6, 2, 4, 1, 4, 5, 2, 2, 5, 6, 3, 6, 2, 4, 2, 5, 6, 3, 4, 3, 6, 1, 4, 5

Offset: 0

Roger L. Bagula, May 13 2005

			[1] -> [2] -> [3,4] -> [2,4,2,5,6] -> [3,4,2,5,6,3,4,3,6,1,4,5] -> ... Lengths of iterates is 1,1,2,5,12,28,... = A034943. - _Michael Somos_

s[1] = {2}; s[2] = {3, 4}; s[3] = {2, 4}; s[4] = {2, 5, 6}; s[5] = {3, 6}; s[6] = {1, 4, 5}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[7]

{a(n)=my(A); if(n<1,0, A=[2]; while(length(A)Michael Somos, May 16 2005 */

1->{2}, 2->{3, 4}, 3->{2, 4}, 4->{2, 5, 6}, 5->{3, 6}, 6->{1, 4, 5}

A216344 Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 .

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 4, 3, 1, 0, 8, 8, 7, 4, 1, 0, 16, 16, 16, 11, 5, 1, 0, 32, 32, 36, 28, 16, 6, 1, 0, 64, 64, 80, 68, 45, 22, 7, 1, 0, 128, 128, 176, 160, 118, 68, 29, 8, 1, 0, 256, 256, 384

Offset: 0

Philippe Deléham, Sep 04 2012

			Triangle begins :
1
0, 1
0, 1, 1
0, 2, 2, 1
0, 4, 4, 3, 1
0, 8, 8, 7, 4, 1
0, 16, 16, 16, 11, 5, 1
0, 32, 32, 36, 28, 16, 6, 1

Cf. A034943

G.f.: (1-2*x+y*x^2)/(1-2*x-y*x+2*y*x^2-y^2*x^3)
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0 and T(n,k) = 0 if k<0 or if k>n .
Sum_{k, 0<=k<=n} T(n,k) = A034943(n+1) .
Sum_{k, 0<=k<=n} T(n,k)*2^k*(-1/2)^(n-k) = A052955(n) .
T(n+1,1) = A011782(n), T(n+2,2) = 2^n = A000079(n), T(n+3,3) = A045891(n+1) .

cp's OEIS Frontend

A106688 Six-symbol substitution: characteristic polynomial: x^6 - 4x^4 - 3x^3 - x - 1.

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A216344 Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 .

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cp's OEIS Frontend

A106688 Six-symbol substitution: characteristic polynomial: x^6 - 4*x^4 - 3*x^3 - x - 1.

Views

Author

Keywords

Examples

Programs

Mathematica

PARI

Formula

A216344 Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 .

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Author

Keywords

Examples

Crossrefs

Formula

A106688 Six-symbol substitution: characteristic polynomial: x^6 - 4x^4 - 3x^3 - x - 1.