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A119727 Triangular array: T(n,k) = T(n,n) = 1, T(n,k) = 5*T(n-1, k-1) + 2*T(n-1, k), read by rows. 4

%I

%S 1,1,1,1,7,1,1,19,37,1,1,43,169,187,1,1,91,553,1219,937,1,1,187,1561,

%T 5203,7969,4687,1,1,379,4057,18211,41953,49219,23437,1,1,763,10009,

%U 56707,174961,308203,292969,117187,1,1,1531,23833,163459,633457,1491211,2126953,1699219,585937,1

%N Triangular array: T(n,k) = T(n,n) = 1, T(n,k) = 5*T(n-1, k-1) + 2*T(n-1, k), read by rows.

%C Second column is A048488. Second diagonal is A057651.

%D TERMESZET VILAGA XI.TERMESZET-TUDOMANY DIAKPALYAZAT 133.EVF. 6.SZ. jun. 2002. Vegh Lea (and Vegh Erika): "Pascal-tipusu haromszogek" http://www.kfki.hu/chemonet/TermVil/tv2002/tv0206/tartalom.html

%H G. C. Greubel, <a href="/A119727/b119727.txt">Rows n = 1..100 of triangle, flattened</a>

%e Triangle begins as:

%e 1;

%e 1, 1;

%e 1, 7, 1;

%e 1, 19, 37, 1;

%e 1, 43, 169, 187, 1;

%e 1, 91, 553, 1219, 937, 1;

%e 1, 187, 1561, 5203, 7969, 4687, 1;

%e 1, 379, 4057, 18211, 41953, 49219, 23437, 1;

%e 1, 763, 10009, 56707, 174961, 308203, 292969, 117187, 1;

%e 1, 1531, 23833, 163459, 633457, 1491211, 2126953, 1699219, 585937, 1;

%p T:= proc(n, k) option remember;

%p if k=1 and k=n then 1

%p else 5*T(n-1, k-1) + 2*T(n-1, k)

%p fi

%p end: seq(seq(T(n, k), k=1..n), n=1..12); # _G. C. Greubel_, Nov 18 2019

%t T[n_, k_]:= T[n, k]= If[k==1 || k==n, 1, 5*T[n-1, k-1] + 2*T[n-1, k]]; Table[T[n,k], {n,10}, {k,n}]//Flatten (* _G. C. Greubel_, Nov 18 2019 *)

%o (PARI) T(n,k) = if(k==1 || k==n, 1, 5*T(n-1,k-1) + 2*T(n-1,k)); \\ _G. C. Greubel_, Nov 18 2019

%o (MAGMA)

%o function T(n,k)

%o if k eq 1 or k eq n then return 1;

%o else return 5*T(n-1,k-1) + 2*T(n-1,k);

%o end if;

%o return T;

%o end function;

%o [T(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Nov 18 2019

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (k==1 or k==n): return 1

%o else: return 5*T(n-1, k-1) + 2*T(n-1, k)

%o [[T(n, k) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Nov 18 2019

%Y Cf. A007318, A048488, A057651, A119725, A119726.

%K easy,nonn,tabl

%O 1,5

%A _Zerinvary Lajos_, Jun 14 2006

%E Edited by _Don Reble_, Jul 24 2006

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)