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 A131061 Triangle read by rows: T(n,k)=4*binom(n,k)-3 (0<=k<=n). 10
 1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 21, 13, 1, 1, 17, 37, 37, 17, 1, 1, 21, 57, 77, 57, 21, 1, 1, 25, 81, 137, 137, 81, 25, 1, 1, 29, 109, 221, 277, 221, 109, 29, 1, 1, 33, 141, 333, 501, 501, 333, 141, 33, 1, 1, 37, 177, 477, 837, 1005, 837, 477, 177, 37, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = A131062: (1, 2, 7, 20, 49, 110, 235,...); the binomial transform of (1, 1, 4, 4, 4,...). 4*A007318 - 3*A000012 as infinite lower triangular matrices. - Emeric Deutsch, Jun 21 2007 LINKS FORMULA G.f.=G(t,z)=(1-z-tz+4tz^2)/[(1-z)(1-tz)(1-z-tz)]. - Emeric Deutsch, Jun 21 2007 EXAMPLE First few rows of the triangle are: 1; 1, 1; 1, 5, 1; 1, 9, 9, 1; 1, 13, 21, 13, 1; 1, 17, 37, 37, 17, 1; 1, 21, 57, 77, 57, 21, 1; ... MAPLE T := proc (n, k) if k <= n then 4*binomial(n, k)-3 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 21 2007 CROSSREFS Cf. A131060, A131062, A131063, A131064, A131065, A131066. Sequence in context: A153108 A157174 A183450 * A157169 A081578 A184883 Adjacent sequences:  A131058 A131059 A131060 * A131062 A131063 A131064 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jun 13 2007 EXTENSIONS More terms from Emeric Deutsch, Jun 21 2007 STATUS approved

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