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!)
 A147703 Triangle [1,1,1,0,0,0,...] DELTA [1,0,0,0,...] with Deléham DELTA defined in A084938. 28
 1, 1, 1, 2, 3, 1, 5, 9, 5, 1, 13, 27, 20, 7, 1, 34, 80, 73, 35, 9, 1, 89, 234, 252, 151, 54, 11, 1, 233, 677, 837, 597, 269, 77, 13, 1, 610, 1941, 2702, 2225, 1199, 435, 104, 15, 1, 1597, 5523, 8533, 7943, 4956, 2158, 657, 135, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Equal to A062110*A007318 when A062110 is regarded as a triangle read by rows. LINKS Indranil Ghosh, Rows 0..100, flattened FORMULA Riordan array ((1-2x)/(1-3x+x^2), x(1-x)/(1-3x+x^2)). Sum_{k=0..n} T(n,k)*x^k = A152239(n), A152223(n), A152185(n), A152174(n), A152167(n), A152166(n), A152163(n), A000007(n), A001519(n), A006012(n), A081704(n), A082761(n), A147837(n), A147838(n), A147839(n), A147840(n), A147841(n), for x = -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively. - Philippe Deléham, Dec 01 2008 G.f.: (1-2*x)/(1-(3+y)*x+(1+y)*x^2). - Philippe Deléham, Nov 26 2011 T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), for n > 1. - Philippe Deléham, Feb 12 2012 The Riordan square of the odd indexed Fibonacci numbers A001519. - Peter Luschny, Jan 26 2020 EXAMPLE Triangle begins 1; 1, 1; 2, 3, 1; 5, 9, 5, 1; 13, 27, 20, 7, 1; 34, 80, 73, 35, 9, 1; 89, 234, 252, 151, 54, 11, 1; MAPLE # The function RiordanSquare is defined in A321620: RiordanSquare(1 / (1 - x / (1 - x / (1 - x))), 10); # Peter Luschny, Jan 26 2020 MATHEMATICA nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 2*x)/(1 - (3 + y)*x + (1 + y)*x^2), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 11 2017 *) CROSSREFS Row sums are A006012. Diagonal sums are A147704. Cf. A062110, A007318, A206800, A001519, A321620. Sequence in context: A293287 A236843 A055905 * A147747 A039599 A154380 Adjacent sequences: A147700 A147701 A147702 * A147704 A147705 A147706 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Nov 10 2008 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 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)