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!)
 A227964 Triangle where the g.f. of row n equals (1-x-x^2+x^3)^n and terms T(n,k) are read by rows n>=0, k=0..3*n. 2
 1, 1, -1, -1, 1, 1, -2, -1, 4, -1, -2, 1, 1, -3, 0, 8, -6, -6, 8, 0, -3, 1, 1, -4, 2, 12, -17, -8, 28, -8, -17, 12, 2, -4, 1, 1, -5, 5, 15, -35, -1, 65, -45, -45, 65, -1, -35, 15, 5, -5, 1, 1, -6, 9, 16, -60, 24, 116, -144, -66, 220, -66, -144, 116, 24, -60, 16, 9, -6, 1, 1, -7, 14, 14, -91, 77, 168, -344, -14, 546, -364, -364, 546, -14, -344, 168, 77, -91, 14, 14, -7, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..2500 FORMULA Sum_{k=0..3*n} |T(n,k)| = A192205(n). Sum_{k=0..3*n} T(n,k)^2 = binomial(4*n,n). Sum_{k=0..3*n} T(n,k) * binomial(3*n,k) = (-1)^n * binomial(4*n,n). Sum_{k=0..3*n} T(n,k) * binomial(2*n+k,k) = 2^n. Sum_{k=0..3*n} T(n,k) * binomial(3*n+k,k) = A008288(3*n,n), where A008288 is the Delannoy array (see A026001). EXAMPLE Triangle begins: 1; 1, -1, -1, 1; 1, -2, -1, 4, -1, -2, 1; 1, -3, 0, 8, -6, -6, 8, 0, -3, 1; 1, -4, 2, 12, -17, -8, 28, -8, -17, 12, 2, -4, 1; 1, -5, 5, 15, -35, -1, 65, -45, -45, 65, -1, -35, 15, 5, -5, 1; 1, -6, 9, 16, -60, 24, 116, -144, -66, 220, -66, -144, 116, 24, -60, 16, 9, -6, 1; 1, -7, 14, 14, -91, 77, 168, -344, -14, 546, -364, -364, 546, -14, -344, 168, 77, -91, 14, 14, -7, 1; ... PROG (PARI) {T(n, k)=polcoeff((1-x-x^2+x^3 +x*O(x^k))^n, k)} for(n=0, 10, for(k=0, 3*n, print1(T(n, k), ", ")); print("")) CROSSREFS Cf. A192205. Sequence in context: A305333 A127772 A086256 * A057550 A324892 A059150 Adjacent sequences:  A227961 A227962 A227963 * A227965 A227966 A227967 KEYWORD sign,tabf AUTHOR Paul D. Hanna, Aug 01 2013 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 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)