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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227076 A triangle formed like Pascal's triangle, but with 5^n on the borders instead of 1. 5
1, 5, 5, 25, 10, 25, 125, 35, 35, 125, 625, 160, 70, 160, 625, 3125, 785, 230, 230, 785, 3125, 15625, 3910, 1015, 460, 1015, 3910, 15625, 78125, 19535, 4925, 1475, 1475, 4925, 19535, 78125, 390625, 97660, 24460, 6400, 2950, 6400, 24460, 97660, 390625 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All rows except the zeroth are divisible by 5. Is there a closed-form formula for these numbers, like for binomial coefficients?

LINKS

T. D. Noe, Rows n = 0..50 of triangle, flattened

FORMULA

T(n,0) = 5^n. T(n,1) = 5*A047850(n-1). T(n,2) = 5*(5^n/80 + 3*n/4 + 51/16). T(n,3) = 5*(5^n/320 + 45*n/16 + 3*n^2/8 + 819/64). - R. J. Mathar, Aug 09 2013

EXAMPLE

Example:

1,

5, 5,

25, 10, 25,

125, 35, 35, 125,

625, 160, 70, 160, 625,

3125, 785, 230, 230, 785, 3125,

15625, 3910, 1015, 460, 1015, 3910, 15625,

78125, 19535, 4925, 1475, 1475, 4925, 19535, 78125,

390625, 97660, 24460, 6400, 2950, 6400, 24460, 97660, 390625

MAPLE

A227076 := proc(n, k)

    if k = 0 or k = n then

        5^n ;

    elif k < 0 or k > n then

        0;

    else

        procname(n-1, k)+procname(n-1, k-1) ;

    end if;

end proc: # R. J. Mathar, Aug 09 2013

MATHEMATICA

t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = 5^n, m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t = Flatten[t]

CROSSREFS

Cf. A007318 (Pascal's triangle), A228053 ((-1)^n on the borders).

Cf. A051601 (n on the borders), A137688 (2^n on borders).

Cf. A083585 (row sums: (8*5^n - 5*2^n)/3), A227074 (4^n edges), A227075 (3^n edges).

Sequence in context: A256693 A255458 A256135 * A223186 A071340 A056451

Adjacent sequences:  A227073 A227074 A227075 * A227077 A227078 A227079

KEYWORD

nonn,tabl

AUTHOR

T. D. Noe, Aug 06 2013

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 02:58 EST 2019. Contains 329383 sequences. (Running on oeis4.)