The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155123 Six levels of the coefficient triangle of the Pascal-Sierpinski functions. 1
 1, 2, 2, 2, 0, 4, 4, 0, -4, 8, 12, 0, 8, -32, 8, 48 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are 2^(n+1); {1, 2, 4, 8, 16, 32,...}. LINKS FORMULA Triangle: {{1}, {1, 1}, {1, 2*n, 1}, {1, f[n], f[n], 1}, {1, g[n], 6 + 24 *(n - 1) + 28*(n - 1)^2 + 8* ( n - 1)^3, g[n], 1}, {1, h[n], k[n - 1] - h[n] - 1, k[n - 1] - h[n] - 1, h[n], 1}} f[n_]=3*n^2 - (n - 1)^2; g[n_]=-2 + 2 *n + 2* n^2 + 2 n^3; h[n_]=-3 + 2 n + 2 n^2 + 2 n^3 + 2*n^4; k[n_]=16+ 80 n + 140 *n^2 + 100*n^3 + 24* n^4; These functions and the triangles they make are general Pascal-Sierpinski functions. EXAMPLE {1}, {2}, {2, 2}, {0, 4, 4}, {0, -4, 8, 12}, {0, 8, -32, 8, 48} MATHEMATICA a1 = {{1}, {1, 1}, {1, 2 *n, 1}, {1, -1 + 2 *n + 2 n^2, -1 + 2 n + 2 n^2, 1}, {1, -2 + 2 *n + 2 n^2 + 2 n^3, 2 - 8 n + 4 n^2 + 8 n^3, -2 + 2* n + 2 n^2 + 2 n^3, 1}, {1, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 1}} Table[CoefficientList[Apply[Plus, a1[[m]]], n], {m, 1, Length[a1]}]; Flatten[%] CROSSREFS Sequence in context: A263527 A261444 A000091 * A125938 A215461 A158851 Adjacent sequences: A155120 A155121 A155122 * A155124 A155125 A155126 KEYWORD tabl,uned,sign AUTHOR Roger L. Bagula, Jan 20 2009 STATUS approved

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

Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)