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 A107448 Irregular triangle T(n, k) = b(n) + k^2 + k + 1, where b(n) = A056486(n-1) - (1/2)*[n=1], for n >= 1 and 1 <= k <= b(n) - 1, read by rows. 3
 5, 7, 11, 17, 13, 17, 23, 31, 41, 53, 67, 83, 101, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Former title: Triangular form sequence made from a version of A082605 Euler extension. REFERENCES Advanced Number Theory, Harvey Cohn, Dover Books, 1963, Page 155 LINKS G. C. Greubel, Rows n = 1..10 of the irregular triangle, flattened FORMULA T(n, k) = b(n) + k^2 + k + 1, where b(n) = A056486(n-1) - (1/2)*[n=1], for n >= 1 and 1 <= k <= b(n) - 1. - G. C. Greubel, Mar 23 2024 EXAMPLE The irregular triangle begins as: 5; 7, 11, 17; 13, 17, 23, 31, 41, 53, 67, 83, 101; 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257; MATHEMATICA (* First program *) a[1] = 3; a[2] = 5; a[3] = 11; a[n_]:= a[n]= Abs[1-4*a[n-2]] -2; euler= Table[a[n], {n, 10}]; Table[k^2 + k + euler[[n]], {n, 7}, {k, euler[[i]] -2}]//Flatten (* Second program *) b[n_]:= 2^(n-3)*(9-(-1)^n) - Boole[n==1]/2; T[n_, k_]:= b[n] +k^2+k+1; Table[T[n, k], {n, 8}, {k, b[n]-1}]//Flatten (* G. C. Greubel, Mar 23 2024 *) PROG (Magma) b:= func< n | n eq 1 select 2 else 2^(n-3)*(9-(-1)^n) >; A107448:= func< n, k | b(n) +k^2 +k +1 >; [A107448(n, k): k in [1..b(n)-1], n in [1..8]]; // G. C. Greubel, Mar 23 2024 (SageMath) def b(n): return 2^(n-3)*(9-(-1)^n) - int(n==1)/2 def A107448(n, k): return b(n) + k^2+k+1; flatten([[A107448(n, k) for k in range(1, b(n))] for n in range(1, 8)]) # G. C. Greubel, Mar 23 2024 CROSSREFS Cf. A056486, A082605. Sequence in context: A072055 A314300 A189320 * A147853 A111226 A168224 Adjacent sequences: A107445 A107446 A107447 * A107449 A107450 A107451 KEYWORD nonn AUTHOR Roger L. Bagula, May 26 2005 EXTENSIONS Edited by G. C. Greubel, Mar 23 2024 STATUS approved

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Last modified April 14 16:59 EDT 2024. Contains 371666 sequences. (Running on oeis4.)