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 A238303 Triangle T(n,k), 0<=k<=n, read by rows given by T(n,0) = 1, T(n,k) = 2 if k>0. 2
 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are A005408(n). Diagonals sums are A109613(n). Sum_{k=0..n} T(n,k)*x^k = A033999(n), A000012(n), A005408(n), A036563(n+2), A058481(n+1), A083584(n), A137410(n), A233325(n), A233326(n), A233328(n), A211866(n+1), A165402(n+1) for x = -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 respectively. Sum_{k=0..n} T(n,k)*x^(n-k) = A151575(n), A000012(n), A040000(n), A005408(n), A033484(n), A048473(n), A020989(n), A057651(n), A061801(n), A238275(n), A238276(n), A138894(n), A090843(n), A199023(n) for x = -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 respectively. Sum_{k=0..n} T(n,k)^x = A000027(n+1), A005408(n), A016813(n), A017077(n) for x = 0, 1, 2, 3 respectively. Sum_{k=0..n} k*T(n,k) = A002378(n). Sum_{k=0..n} A000045(k)*T(n,k) = A019274(n+2). Sum_{k=0..n} A000142(k)*T(n,k) = A066237(n+1). LINKS FORMULA T(n,0) = A000012(n) = 1, T(n+k,k) = A007395(n) = 2 for k>0. EXAMPLE Triangle begins: 1; 1, 2; 1, 2, 2; 1, 2, 2, 2; 1, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2; 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2; ... CROSSREFS Cf. Diagonals: A040000. Cf. Columns: A000012, A007395. First differences of A001614. Sequence in context: A274353 A183028 A114284 * A023575 A215113 A058978 Adjacent sequences: A238300 A238301 A238302 * A238304 A238305 A238306 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 24 2014 STATUS approved

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Last modified December 7 12:12 EST 2022. Contains 358656 sequences. (Running on oeis4.)