A213567
Principal diagonal of the convolution array A213566.
Original entry on oeis.org
1, 13, 59, 183, 476, 1108, 2409, 4993, 10007, 19559, 37504, 70832, 132145, 244029, 446763, 811847, 1465676, 2630836, 4697945, 8350305, 14779671, 26058903, 45784224, 80179968, 139995361, 243755533, 423324539, 733409943
Offset: 1
- Clark Kimberling, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-12,5,12,-12,-3,6,0,-1).
-
F:=Fibonacci;; List([1..30], n-> (2*n+3)*F(n+3)+(n^2+2)*F(n+2) -4*(n^2+2*n+2)); # G. C. Greubel, Jul 26 2019
-
F:= Fibonacci; [(2*n+3)*F(n+3)+(n^2+2)*F(n+2) -4*(n^2+2*n+2): n in [1..30]]; // G. C. Greubel, Jul 26 2019
-
(* First program *)
b[n_]:= Fibonacci[n]; c[n_]:= n^2;
t[n_, k_]:= Sum[b[k-i] c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:= Table[t[n, k], {k, 1, 60}] (* A213566 *)
d = Table[t[n, n], {n, 1, 40}] (* A213567 *)
s[n_]:= Sum[t[i, n+1-i], {i, 1, n}]
s1 = Table[s[n], {n, 1, 50}] (* A213570 *)
(* Second program *)
Table[(2*n+3)*Fibonacci[n+3] +(n^2+2)*Fibonacci[n+2] -4*(n^2+2*n+2), {n, 30}] (* G. C. Greubel, Jul 26 2019 *)
-
vector(30, n, f=fibonacci; (2*n+3)*f(n+3)+(n^2+2)*f(n+2) -4*(n^2+ 2*n+2)) \\ G. C. Greubel, Jul 26 2019
-
f=fibonacci; [(2*n+3)*f(n+3)+(n^2+2)*f(n+2) -4*(n^2+ 2*n+2) for n in (1..30)] # G. C. Greubel, Jul 26 2019
A213570
Antidiagonal sums of the convolution array A213566.
Original entry on oeis.org
1, 9, 37, 110, 272, 598, 1213, 2323, 4265, 7588, 13184, 22500, 37881, 63125, 104381, 171602, 280896, 458330, 746085, 1212415, 1967761, 3190824, 5170752, 8375400, 13561777, 21954753, 35536213, 57512918, 93073520, 150613438
Offset: 1
-
List([1..35], n-> Fibonacci(n+9)+Lucas(1,-1,n+8)[2] -(n^3+9*n^2 +39*n+81)); # G. C. Greubel, Jul 26 2019
-
[Fibonacci(n+9) +Lucas(n+8) -(n^3+9*n^2+39*n+81): n in [1..35]]; // G. C. Greubel, Jul 26 2019
-
(* First program *)
b[n_]:= Fibonacci[n]; c[n_]:= n^2;
t[n_, k_]:= Sum[b[k-i] c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:= Table[t[n, k], {k, 1, 60}] (* A213566 *)
d = Table[t[n, n], {n, 1, 40}] (* A213567 *)
s[n_]:= Sum[t[i, n+1-i], {i, 1, n}]
s1 = Table[s[n], {n, 1, 50}] (* A213570 *)
(* Second program *)
Table[Fibonacci[n+9] + LucasL[n+8] -(n^3+9*n^2+39*n+81), {n,35}] (* G. C. Greubel, Jul 26 2019 *)
-
vector(35,n, f=fibonacci; 2*f(n+9)+f(n+7) -(n^3+9*n^2+39*n+81)) \\ G. C. Greubel, Jul 26 2019
-
[fibonacci(n+9) +lucas_number2(n+8,1,-1) -(n^3+9*n^2+39*n+81) for n in (1..35)] # G. C. Greubel, Jul 26 2019
A213500
Rectangular array T(n,k): (row n) = b**c, where b(h) = h, c(h) = h + n - 1, n >= 1, h >= 1, and ** = convolution.
Original entry on oeis.org
1, 4, 2, 10, 7, 3, 20, 16, 10, 4, 35, 30, 22, 13, 5, 56, 50, 40, 28, 16, 6, 84, 77, 65, 50, 34, 19, 7, 120, 112, 98, 80, 60, 40, 22, 8, 165, 156, 140, 119, 95, 70, 46, 25, 9, 220, 210, 192, 168, 140, 110, 80, 52, 28, 10, 286, 275, 255, 228, 196, 161, 125, 90
Offset: 1
Northwest corner (the array is read by southwest falling antidiagonals):
1, 4, 10, 20, 35, 56, 84, ...
2, 7, 16, 30, 50, 77, 112, ...
3, 10, 22, 40, 65, 98, 140, ...
4, 13, 28, 50, 80, 119, 168, ...
5, 16, 34, 60, 95, 140, 196, ...
6, 19, 40, 70, 110, 161, 224, ...
T(6,1) = (1)**(6) = 6;
T(6,2) = (1,2)**(6,7) = 1*7+2*6 = 19;
T(6,3) = (1,2,3)**(6,7,8) = 1*8+2*7+3*6 = 40.
-
b[n_] := n; c[n_] := n
t[n_, k_] := Sum[b[k - i] c[n + i], {i, 0, k - 1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}]]
r[n_] := Table[t[n, k], {k, 1, 60}] (* A213500 *)
-
t(n,k) = sum(i=0, k - 1, (k - i) * (n + i));
tabl(nn) = {for(n=1, nn, for(k=1, n, print1(t(k,n - k + 1),", ");); print(););};
tabl(12) \\ Indranil Ghosh, Mar 26 2017
-
def t(n, k): return sum((k - i) * (n + i) for i in range(k))
for n in range(1, 13):
print([t(k, n - k + 1) for k in range(1, n + 1)]) # Indranil Ghosh, Mar 26 2017
Showing 1-3 of 3 results.
Comments