This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155998 Triangle read by rows: T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 - (-1)^k)/2. 1
 0, 1, 1, 0, 4, 0, 1, 3, 3, 1, 0, 8, 0, 8, 0, 1, 5, 10, 10, 5, 1, 0, 12, 0, 40, 0, 12, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 16, 0, 112, 0, 112, 0, 16, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 20, 0, 240, 0, 504, 0, 240, 0, 20, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: A155559(n) = {0, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...}. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 - (-1)^k)/2. From G. C. Greubel, Dec 01 2019: (Start) T(n, k) = binomial(n, k)*(2 - (-1)^k*(1 + (-1)^n))/2. Sum_{k=0..n} T(n,k) = 2^n = A155559(n) for n >= 1. Sum_{k=0..n-1} T(n,k) = (2^(n+1) - (1-(-1)^n))/2 = A051049(n), n >= 1. (End) EXAMPLE Triangle begins as:   0;   1,  1;   0,  4,  0;   1,  3,  3,   1;   0,  8,  0,   8,   0;   1,  5, 10,  10,   5,   1;   0, 12,  0,  40,   0,  12,  0;   1,  7, 21,  35,  35,  21,  7,   1;   0, 16,  0, 112,   0, 112,  0,  16, 0;   1,  9, 36,  84, 126, 126, 84,  36, 9,  1;   0, 20,  0, 240,   0, 504,  0, 240, 0, 20, 0; MAPLE seq(seq( binomial(n, k)*(2 - (-1)^k*(1+(-1)^n))/2, k=0..n), n=0..12); # G. C. Greubel, Dec 01 2019 MATHEMATICA f[n_, k_]:= Binomial[n, k]*(1 - (-1)^k)/2; Table[f[n, k]+f[n, n-k], {n, 0, 10}, {k, 0, n}]//Flatten Table[Binomial[n, k]*(2-(-1)^k*(1+(-1)^n))/2, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Dec 01 2019 *) PROG (PARI) T(n, k) = binomial(n, k)*(2 - (-1)^k*(1+(-1)^n))/2; \\ G. C. Greubel, Dec 01 2019 (MAGMA) [Binomial(n, k)*(2 - (-1)^k*(1+(-1)^n))/2: k in [0..n], n in [0..12]]; // G. C. Greubel, Dec 01 2019 (Sage) [[binomial(n, k)*(2 - (-1)^k*(1+(-1)^n))/2 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Dec 01 2019 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)*(2 - (-1)^k*(1 + (-1)^n))/2 ))); # G. C. Greubel, Dec 01 2019 CROSSREFS Sequence in context: A229987 A307769 A096793 * A298063 A298712 A127538 Adjacent sequences:  A155995 A155996 A155997 * A155999 A156000 A156001 KEYWORD nonn,tabl,changed AUTHOR Roger L. Bagula, Feb 01 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)