The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102752 Array read by antidiagonals: T(n, k) = ((n+2)^k-(n-1)^k)/3. 0
 0, 0, 1, 0, 1, 1, 0, 1, 3, 3, 0, 1, 5, 9, 5, 0, 1, 7, 21, 27, 11, 0, 1, 9, 39, 85, 81, 21, 0, 1, 11, 63, 203, 341, 243, 43, 0, 1, 13, 93, 405, 1031, 1365, 729, 85, 0, 1, 15, 129, 715, 2511, 5187, 5461, 2187, 171, 0, 1, 17, 171, 1157, 5261, 15309, 25999, 21845, 6561, 341, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Consider a 3 X 3 matrix M = [n, 1, 1] [1, n, 1] [1, 1, n]. The n-th row of the array contains the values of the nondiagonal elements of M^k, k=0,1,.... (Corresponding diagonal entry = nondiagonal entry + (n-1)^k.) Table: n: row sequence G.f. cross references. 0: (2^n-(-1)^n)/3 1/((1+1x)(1-2x)) A001045 (Jacobsthal sequence) 1: (3^n-0^n)/3 1/(1-3x)) A000244 2: (4^n-1^n)/3 1/((1-1x)(1-4x)) A002450 3: (5^n-2^n)/3 1/((1-2x)(1-5x)) A016127 4: (6^n-3^n)/3 1/((1-3x)(1-6x)) A016137 5: (7^n-4^n)/3 1/((1-4x)(1-7x)) A016150 6: (8^n-5^n)/3 1/((1-5x)(1-8x)) A016162 7: (9^n-6^n)/3 1/((1-6x)(1-9x)) A016172 8: (10^n-7^n)/3 1/((1-7x)(1-10x)) A016181 9: (11^n-8^n)/3 1/((1-8x)(1-11x)) A016187 10:(12^n-9^n)/3 1/((1-9x)(1-12x)) A016191 If r(n) denotes a row sequence, r(n+1)/r(n) converges to n+2. Columns follow polynomials with certain binomial coefficients: column: polynomial 0; 0 1: 1 2: 2*n + 1 3: 3*n^2+ 3*n + 3 4: 4*n^3+ 6*n^2+ 12*n + 5 5: 5*n^4+10*n^3+ 30*n^2+ 25*n + 11 6: 6*n^5+15*n^4+ 60*n^3+ 75*n^2+ 66*n + 21 7: 7*n^6+21*n^5+105*n^4+ 175*n^3+ 231*n^2+ 147*n + 43 8: 8*n^7+28*n^6+168*n^5+ 350*n^4+ 616*n^3+ 588*n^2+344*n+ 85 etc. Coefficients are generated by the array T(n,k)=(2^(n-k-1)-(-1)^(n-k-1))/3*(binomial(k+(n-k-1),n-k-1)) read by antidiagonals. LINKS EXAMPLE Array begins:   0, 1, 1,  3,   5,   11, ...   0, 1, 3,  9,  27,   81, ...   0, 1, 5, 21,  85,  341, ...   0, 1, 7, 39, 203, 1031, ...   0, 1, 9, 63, 405, 2511, ...   ... PROG (PARI) MM(n, N)=local(M); M=matrix(n, n); for(i=1, n, for(j=1, n, if(i==j, M[i, j]=N, M[i, j]=1))); M for(k=0, 10, for(i=0, 10, print1((MM(3, k)^i)[1, 2], ", ")); print()) CROSSREFS Sequence in context: A306629 A185282 A193470 * A104548 A085707 A320253 Adjacent sequences:  A102749 A102750 A102751 * A102753 A102754 A102755 KEYWORD nonn,tabl AUTHOR Lambert Klasen (lambert.klasen(AT)gmx.net) and Gary W. Adamson, Feb 09 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)