login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213587 Rectangular array:  (row n) = b**c, where b(h) = F(h+1), c(h) = F(n+h), F = A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution. 7
1, 4, 2, 10, 7, 3, 22, 17, 11, 5, 45, 37, 27, 18, 8, 88, 75, 59, 44, 29, 13, 167, 146, 120, 96, 71, 47, 21, 310, 276, 234, 195, 155, 115, 76, 34, 566, 511, 443, 380, 315, 251, 186, 123, 55, 1020, 931, 821, 719, 614, 510, 406, 301, 199, 89, 1819, 1675 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Principal diagonal: A213588.

Antidiagonal sums: A213589.

Row 1,  (1,2,3,5,...)**(1,2,3,5,...): A004798.

Row 2,  (1,2,3,5,...)**(2,3,5,8,...)

Row 3,  (1,2,3,5,...)**(3,5,8,13,...)

For a guide to related arrays, see A213500.

LINKS

Clark Kimberling, Antidiagonals n = 1..60, flattened

FORMULA

Rows:  T(n,k) = 2*T(n,k-1)+T(n,k-2)-2*T(n,k-3)-T(n,k-4).

Columns:  T(n,k)=T(n-1,k) + T(n-2,k).

G.f. for row n:  f(x)/g(x), where f(x) = F(n+1) + F(n+2)*x + F(n)*x^2 and g(x) = (1 - x - x^2)^2.

EXAMPLE

Northwest corner (the array is read by falling antidiagonals):

1....4....10....22....45....88....167

2....7....17....37....75....146...276

3....11...27....59....120...234...443

5....18...44....96....195...380...719

8....29...71....155...315...614...1162

12...47...115...251...510...994...1881

MATHEMATICA

b[n_] := Fibonacci[n + 1]; c[n_] := Fibonacci[n + 1];

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}]  (* A213587 *)

Table[t[n, n], {n, 1, 40}] (* A213588 *)

s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}]

Table[s[n], {n, 1, 50}] (* A213589 *)

CROSSREFS

Cf. A213500.

Sequence in context: A160572 A213500 A213584 * A066579 A117821 A266851

Adjacent sequences:  A213584 A213585 A213586 * A213588 A213589 A213590

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Jun 19 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 21:33 EST 2016. Contains 278755 sequences.